Parallel structure usually refers to clauses, but here the closest is D, which contains parallel predicates, or verb phrases. A. is simply multiple subjects (here, gerunds--nouns ending in -ing, naming actions). B. is multiple verbs. C. is multiple gerunds in the object slot. Parallel constructions of any kind denote structural patterns in the thinking process that produced the utterance. Just like repeated patterns in songs, or designs, or organizations, they infer an order, a unity in the world, different from uniqueness.

D. for parallelism means having words, phrases, or clauses analogous to each other. In A, the third is a gerund phrase. In B, the second is a gerund. And, in C, the third is also a phrase, which i think is not even analogous to the first two. So, option D properly used parallelism. :)